SQRT01
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n
matrix A, and partially tests SORGQR which forms the m-by-m
orthogonal matrix Q.
SQRT01 compares R with Q'*A, and checks that Q is orthogonal.
matrix A, and partially tests SORGQR which forms the m-by-m
orthogonal matrix Q.
SQRT01 compares R with Q'*A, and checks that Q is orthogonal.
Arguments
| M |
(input) INTEGER
The number of rows of the matrix A. M >= 0.
|
| N |
(input) INTEGER
The number of columns of the matrix A. N >= 0.
|
| A |
(input) REAL array, dimension (LDA,N)
The m-by-n matrix A.
|
| AF |
(output) REAL array, dimension (LDA,N)
Details of the QR factorization of A, as returned by SGEQRF.
See SGEQRF for further details. |
| Q |
(output) REAL array, dimension (LDA,M)
The m-by-m orthogonal matrix Q.
|
| R |
(workspace) REAL array, dimension (LDA,max(M,N))
|
| LDA |
(input) INTEGER
The leading dimension of the arrays A, AF, Q and R.
LDA >= max(M,N). |
| TAU |
(output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by SGEQRF. |
| WORK |
(workspace) REAL array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The dimension of the array WORK.
|
| RWORK |
(workspace) REAL array, dimension (M)
|
| RESULT |
(output) REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) |